Fluorescence competition and optical melting measurements of RNA three-way multibranch loops provide a revised model for thermodynamic parameters

The Metabolome Weakens RNA Thermodynamic Stability and Strengthens RNA Chemical Stability

We examined the complex network of interactions among RNA, the metabolome, and divalent Mg2+ under conditions that mimic the Escherichia coli cytoplasm. We determined Mg2+ binding constants for the top 15 E. coli metabolites, comprising 80% of the metabolome by concentration at physiological pH and monovalent ion concentrations. These data were used to inform the development of an artificial cytoplasm that mimics in vivo E. coli conditions, which we term "Eco80". We empirically determined that the mixture of E. coli metabolites in Eco80 approximated single-site binding behavior toward Mg2+ in the biologically relevant free Mg2+ range of ∼0.5 to 3 mM Mg2+, using a Mg2+-sensitive fluorescent dye. Effects of Eco80 conditions on the thermodynamic stability, chemical stability, structure, and catalysis of RNA were examined. We found that Eco80 conditions lead to opposing effects on the thermodynamic and chemical stabilities of RNA. In particular, the thermodynamic stability of RNA helices was weakened by 0.69 ± 0.12 kcal/mol, while the chemical stability was enhanced ∼2-fold, which can be understood using the speciation of Mg2+ between weak and strong Mg2+-metabolite complexes in Eco80. Overall, the use of Eco80 reflects RNA function in vivo and enhances the biological relevance of mechanistic studies of RNA.

A Test and Refinement of Folding Free Energy Nearest Neighbor Parameters for RNA Including N6-Methyladenosine

RNA folding free energy change parameters are widely used to predict RNA secondary structure and to design RNA sequences. These parameters include terms for the folding free energies of helices and loops. Although the full set of parameters has only been traditionally available for the four common bases and backbone, it is well known that covalent modifications of nucleotides are widespread in natural RNAs. Covalent modifications are also widely used in engineered sequences. We recently derived a full set of nearest neighbor terms for RNA that includes N6-methyladenosine (m6A). In this work, we test the model using 98 optical melting experiments, matching duplexes with or without N6-methylation of A. Most experiments place RRACH, the consensus site of N6-methylation, in a variety of contexts, including helices, bulge loops, internal loops, dangling ends, and terminal mismatches. For matched sets of experiments that include either A or m6A in the same context, we find that the parameters for m6A are as accurate as those for A. Across all experiments, the root mean squared deviation between estimated and experimental free energy changes is 0.67 kcal/mol. We used the new experimental data to refine the set of nearest neighbor parameter terms for m6A. These parameters enable prediction of RNA secondary structures including m6A, which can be used to model how N6-methylation of A affects RNA structure.

VfoldMCPX: predicting multistrand RNA complexes

Multistrand RNA complexes play a critical role in RNA-related biological processes. The understanding of RNA functions and the rational design of RNA nanostructures require accurate prediction of the structure and folding stability of the complexes, including those containing pseudoknots. Here, we present VfoldMCPX, a new model for predicting two-dimensional (2D) structures and folding stabilities of multistrand RNA complexes. Based on a partition function-based algorithm combined with physical loop free energy parameters, the VfoldMCPX model predicts not only the native structure but also the folding stability of the complex. An important advantage of the model is the ability to treat pseudoknotted structures. Extensive tests on structure predictions show the VfoldMCPX model provides improved accuracy for multistranded RNA complexes, especially for RNA complexes with three or more strands and/or containing pseudoknots. We have developed a freely accessible VfoldMCPX web server at http://rna.physics.missouri.edu/vfoldMCPX2.

Fluorescence-Based Binding Characterization of Small Molecule Ligands Targeting CUG RNA Repeats

Pathogenic CUG and CCUG RNA repeats have been associated with myotonic dystrophy type 1 and 2 (DM1 and DM2), respectively. Identifying small molecules that can bind these RNA repeats is of great significance to develop potential therapeutics to treat these neurodegenerative diseases. Some studies have shown that aminoglycosides and their derivatives could work as potential lead compounds targeting these RNA repeats. In this work, sisomicin, previously known to bind HIV-1 TAR, is investigated as a possible ligand for CUG RNA repeats. We designed a novel fluorescence-labeled RNA sequence of r(CUG)10 to mimic cellular RNA repeats and improve the detecting sensitivity. The interaction of sisomicin with CUG RNA repeats is characterized by the change of fluorescent signal, which is initially minimized by covalently incorporating the fluorescein into the RNA bases and later increased upon ligand binding. The results show that sisomicin can bind and stabilize the folded RNA structure. We demonstrate that this new fluorescence-based binding characterization assay is consistent with the classic UV Tm technique, indicating its feasibility for high-throughput screening of ligand-RNA binding interactions and wide applications to measure the thermodynamic parameters in addition to binding constants and kinetics when probing such interactions.

Challenges with Simulating Modified RNA: Insights into Role and Reciprocity of Experimental and Computational Approaches

RNA is critical to a broad spectrum of biological and viral processes. This functional diversity is a result of their dynamic nature; the variety of three-dimensional structures that they can fold into; and a host of post-transcriptional chemical modifications. While there are many experimental techniques to study the structural dynamics of biomolecules, molecular dynamics simulations (MDS) play a significant role in complementing experimental data and providing mechanistic insights. The accuracy of the results obtained from MDS is determined by the underlying physical models i.e., the force-fields, that steer the simulations. Though RNA force-fields have received a lot of attention in the last decade, they still lag compared to their protein counterparts. The chemical diversity imparted by the RNA modifications adds another layer of complexity to an already challenging problem. Insight into the effect of RNA modifications upon RNA folding and dynamics is lacking due to the insufficiency or absence of relevant experimental data. This review provides an overview of the state of MDS of modified RNA, focusing on the challenges in parameterization of RNA modifications as well as insights into relevant reference experiments necessary for their calibration.

Chimeric RNA Design Principles for RNA-Mediated Gene Fusion

One common genetic alteration in cancer is gene fusion resulting from chromosomal translocations. The mechanisms that create such oncogenic fusion genes are not well understood. Previously, we provided the direct evidence that expression of a designed chimeric RNA can drive the formation of TMPRSS2-ERG gene fusion. Central to this RNA-mediated gene fusion mechanism is a proposed three-way junction formed by RNA/DNA hybrid and the intergenic DNA stem formed by target genes. In this study, we determined the important parameters for chimeric RNA-mediated gene fusion using TMPRSS2-ERG fusion gene as the model. Our results indicate that both the chimeric RNA lengths and the sizes of unpaired bulges play important roles in inducing TMPRSS2-ERG gene fusion. The optimal length of unpaired bulges was about 35 nt, while the optimal chimeric RNA length was about 50 nt for targeting. These observations were consistent regardless of the target locations within TMPRSS2 and ERG genes. These empirically determined parameters provide important insight for searching cellular RNAs that may initiate oncogenic fusion genes. The knowledge could also facilitate the development of useful genomic technology for manipulating mammalian genomes.

Vfold2D-MC: A Physics-Based Hybrid Model for Predicting RNA Secondary Structure Folding

Accurate prediction of RNA structure and folding stability has a far-reaching impact on our understanding of RNA functions. Here we develop Vfold2D-MC, a new physics-based model, to predict RNA structure and folding thermodynamics from the sequence. The model employs virtual bond-based coarse-graining of RNA backbone conformation and generates RNA conformations through Monte Carlo sampling of the bond angles and torsional angles of the virtual bonds. Using a coarse-grained statistical potential derived from the known structures, we assign each conformation with a statistical weight. The weighted average over the conformational ensemble gives the entropy and free energy parameters for the hairpin, bulge, and internal loops, and multiway junctions. From the thermodynamic parameters, we predict RNA structures, melting curves, and structural changes from the sequence. Theory-experiment comparisons indicate that Vfold2D-MC not only gives improved structure predictions but also enables the interpretation of thermodynamic results for different RNA structures, including multibranched junctions. This new model sets a promising framework to treat more complicated RNA structures, such as pseudoknotted and intramolecular kissing loops, for which experimental thermodynamic parameters are often unavailable.

Determining parameters for non-linear models of multi-loop free energy change

MOTIVATION

Predicting the secondary structure of RNA is a fundamental task in bioinformatics. Algorithms that predict secondary structure given only the primary sequence, and a model to evaluate the quality of a structure, are an integral part of this. These algorithms have been updated as our model of RNA thermodynamics changed and expanded. An exception to this has been the treatment of multi-loops. Although more advanced models of multi-loop free energy change have been suggested, a simple, linear model has been used since the 1980s. However, recently, new dynamic programing algorithms for secondary structure prediction that could incorporate these models were presented. Unfortunately, these models appear to have lower accuracy for secondary structure prediction.

RESULTS

We apply linear regression and a new parameter optimization algorithm to find better parameters for the existing linear model and advanced non-linear multi-loop models. These include the Jacobson-Stockmayer and Aalberts & Nandagopal models. We find that the current linear model parameters may be near optimal for the linear model, and that no advanced model performs better than the existing linear model parameters even after parameter optimization.

AVAILABILITY AND IMPLEMENTATION

Source code and data is available at https://github.com/maxhwardg/advanced_multiloops.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Analysis of RNA nearest neighbor parameters reveals interdependencies and quantifies the uncertainty in RNA secondary structure prediction

RNA secondary structure prediction is often used to develop hypotheses about structure-function relationships for newly discovered RNA sequences, to identify unknown functional RNAs, and to design sequences. Secondary structure prediction methods typically use a thermodynamic model that estimates the free energy change of possible structures based on a set of nearest neighbor parameters. These parameters were derived from optical melting experiments of small model oligonucleotides. This work aims to better understand the precision of structure prediction. Here, the experimental errors in optical melting experiments were propagated to errors in the derived nearest neighbor parameter values and then to errors in RNA secondary structure prediction. To perform this analysis, the optical melting experimental values were systematically perturbed within the estimates of experimental error and alternative sets of nearest neighbor parameters were then derived from these error-bounded values. Secondary structure predictions using either the perturbed or reference parameter sets were then compared. This work demonstrated that the precision of RNA secondary structure prediction is more robust than suggested by previous work based on perturbation of the nearest neighbor parameters. This robustness is due to correlations between parameters. Additionally, this work identified weaknesses in the parameter derivation that makes accurate assessment of parameter uncertainty difficult. Considerations for experimental design are provided to mitigate these weaknesses are provided.

A sensitivity analysis of RNA folding nearest neighbor parameters identifies a subset of free energy parameters with the greatest impact on RNA secondary structure prediction

Nearest neighbor parameters for estimating the folding energy changes of RNA secondary structures are used in structure prediction and analysis. Despite their widespread application, a comprehensive analysis of the impact of each parameter on the precision of calculations had not been conducted. To identify the parameters with greatest impact, a sensitivity analysis was performed on the 291 parameters that compose the 2004 version of the free energy nearest neighbor rules. Perturbed parameter sets were generated by perturbing each parameter independently. Then the effect of each individual parameter change on predicted base-pair probabilities and secondary structures as compared to the standard parameter set was observed for a set of sequences including structured ncRNA, mRNA and randomized sequences. The results identify for the first time the parameters with the greatest impact on secondary structure prediction, and the subset which should be prioritized for further study in order to improve the precision of structure prediction. In particular, bulge loop initiation, multibranch loop initiation, AU/GU internal loop closure and AU/GU helix end parameters were particularly important. An analysis of parameter usage during folding free energy calculations of stochastic samples of secondary structures revealed a correlation between parameter usage and impact on structure prediction precision.

Thermodynamic stabilities of three-way junction nanomotifs in prohead RNA

The thermodynamic stabilities of four natural prohead or packaging RNA (pRNA) three-way junction (3WJ) nanomotifs and seven phi29 pRNA 3WJ deletion mutant nanomotifs were investigated using UV optical melting on a three-component RNA system. Our data reveal that some pRNA 3WJs are more stable than the phi29 pRNA 3WJ. The stability of the 3WJ contributes to the unique self-assembly properties of pRNA. Thus, ultrastable pRNA 3WJ motifs suggest new scaffolds for pRNA-based nanotechnology. We present data demonstrating that pRNA 3WJs differentially respond to the presence of metal ions. A comparison of our data with free energies predicted by currently available RNA secondary structure prediction programs shows that these programs do not accurately predict multibranch loop stabilities. These results will expand the existing parameters used for RNA secondary structure prediction from sequence in order to better inform RNA structure-function hypotheses and guide the rational design of functional RNA supramolecular assemblies.

Blind tests of RNA nearest-neighbor energy prediction

The predictive modeling and design of biologically active RNA molecules requires understanding the energetic balance among their basic components. Rapid developments in computer simulation promise increasingly accurate recovery of RNA's nearest-neighbor (NN) free-energy parameters, but these methods have not been tested in predictive trials or on nonstandard nucleotides. Here, we present, to our knowledge, the first such tests through a RECCES-Rosetta (reweighting of energy-function collection with conformational ensemble sampling in Rosetta) framework that rigorously models conformational entropy, predicts previously unmeasured NN parameters, and estimates these values' systematic uncertainties. RECCES-Rosetta recovers the 10 NN parameters for Watson-Crick stacked base pairs and 32 single-nucleotide dangling-end parameters with unprecedented accuracies: rmsd of 0.28 kcal/mol and 0.41 kcal/mol, respectively. For set-aside test sets, RECCES-Rosetta gives rmsd values of 0.32 kcal/mol on eight stacked pairs involving G-U wobble pairs and 0.99 kcal/mol on seven stacked pairs involving nonstandard isocytidine-isoguanosine pairs. To more rigorously assess RECCES-Rosetta, we carried out four blind predictions for stacked pairs involving 2,6-diaminopurine-U pairs, which achieved 0.64 kcal/mol rmsd accuracy when tested by subsequent experiments. Overall, these results establish that computational methods can now blindly predict energetics of basic RNA motifs, including chemically modified variants, with consistently better than 1 kcal/mol accuracy. Systematic tests indicate that resolving the remaining discrepancies will require energy function improvements beyond simply reweighting component terms, and we propose further blind trials to test such efforts.

Bridging the gap between in vitro and in vivo RNA folding

Deciphering the folding pathways and predicting the structures of complex three-dimensional biomolecules is central to elucidating biological function. RNA is single-stranded, which gives it the freedom to fold into complex secondary and tertiary structures. These structures endow RNA with the ability to perform complex chemistries and functions ranging from enzymatic activity to gene regulation. Given that RNA is involved in many essential cellular processes, it is critical to understand how it folds and functions in vivo. Within the last few years, methods have been developed to probe RNA structures in vivo and genome-wide. These studies reveal that RNA often adopts very different structures in vivo and in vitro, and provide profound insights into RNA biology. Nonetheless, both in vitro and in vivo approaches have limitations: studies in the complex and uncontrolled cellular environment make it difficult to obtain insight into RNA folding pathways and thermodynamics, and studies in vitro often lack direct cellular relevance, leaving a gap in our knowledge of RNA folding in vivo. This gap is being bridged by biophysical and mechanistic studies of RNA structure and function under conditions that mimic the cellular environment. To date, most artificial cytoplasms have used various polymers as molecular crowding agents and a series of small molecules as cosolutes. Studies under such in vivo-like conditions are yielding fresh insights, such as cooperative folding of functional RNAs and increased activity of ribozymes. These observations are accounted for in part by molecular crowding effects and interactions with other molecules. In this review, we report milestones in RNA folding in vitro and in vivo and discuss ongoing experimental and computational efforts to bridge the gap between these two conditions in order to understand how RNA folds in the cell.

An introduction to recurrent nucleotide interactions in RNA

RNA secondary structure diagrams familiar to molecular biologists summarize at a glance the folding of RNA chains to form Watson–Crick paired double helices. However, they can be misleading: First of all, they imply that the nucleotides in loops and linker segments, which can amount to 35% to 50% of a structured RNA, do not significantly interact with other nucleotides. Secondly, they give the impression that RNA molecules are loosely organized in three-dimensional (3D) space. In fact, structured RNAs are compactly folded as a result of numerous long-range, sequence-specific interactions, many of which involve loop or linker nucleotides. Here, we provide an introduction for students and researchers of RNA on the types, prevalence, and sequence variations of inter-nucleotide interactions that structure and stabilize RNA 3D motifs and architectures, using Escherichia coli (E. coli) 16S ribosomal RNA as a concrete example. The picture that emerges is that almost all nucleotides in structured RNA molecules, including those in nominally single-stranded loop or linker regions, form specific interactions that stabilize functional structures or mediate interactions with other molecules. The small number of noninteracting, ‘looped-out’ nucleotides make it possible for the RNA chain to form sharp turns. Base-pairing is the most specific interaction in RNA as it involves edge-to-edge hydrogen bonding (H-bonding) of the bases. Non-Watson–Crick base pairs are a significant fraction (30% or more) of base pairs in structured RNAs.

The determination of RNA folding nearest neighbor parameters

The stability of RNA secondary structure can be predicted using a set of nearest neighbor parameters. These parameters are widely used by algorithms that predict secondary structure. This contribution introduces the UV optical melting experiments that are used to determine the folding stability of short RNA strands. It explains how the nearest neighbor parameters are chosen and how the values are fit to the data. A sample nearest neighbor calculation is provided. The contribution concludes with new methods that use the database of sequences with known structures to determine parameter values.

The four ingredients of single-sequence RNA secondary structure prediction. A unifying perspective

Any method for RNA secondary structure prediction is determined by four ingredients. The architecture is the choice of features implemented by the model (such as stacked basepairs, loop length distributions, etc.). The architecture determines the number of parameters in the model. The scoring scheme is the nature of those parameters (whether thermodynamic, probabilistic, or weights). The parameterization stands for the specific values assigned to the parameters. These three ingredients are referred to as "the model." The fourth ingredient is the folding algorithms used to predict plausible secondary structures given the model and the sequence of a structural RNA. Here, I make several unifying observations drawn from looking at more than 40 years of methods for RNA secondary structure prediction in the light of this classification. As a final observation, there seems to be a performance ceiling that affects all methods with complex architectures, a ceiling that impacts all scoring schemes with remarkable similarity. This suggests that modeling RNA secondary structure by using intrinsic sequence-based plausible "foldability" will require the incorporation of other forms of information in order to constrain the folding space and to improve prediction accuracy. This could give an advantage to probabilistic scoring systems since a probabilistic framework is a natural platform to incorporate different sources of information into one single inference problem.

Squaring theory with practice in RNA design

Ribonucleic acid (RNA) design offers unique opportunities for engineering genetic networks and nanostructures that self-assemble within living cells. Recent years have seen the creation of increasingly complex RNA devices, including proof-of-concept applications for in vivo three-dimensional scaffolding, imaging, computing, and control of biological behaviors. Expert intuition and simple design rules--the stability of double helices, the modularity of noncanonical RNA motifs, and geometric closure--have enabled these successful applications. Going beyond heuristics, emerging algorithms may enable automated design of RNAs with nucleotide-level accuracy but, as illustrated on a recent RNA square design, are not yet fully predictive. Looking ahead, technological advances in RNA synthesis and interrogation are poised to radically accelerate the discovery and stringent testing of design methods.

A range of complex probabilistic models for RNA secondary structure prediction that includes the nearest-neighbor model and more

The standard approach for single-sequence RNA secondary structure prediction uses a nearest-neighbor thermodynamic model with several thousand experimentally determined energy parameters. An attractive alternative is to use statistical approaches with parameters estimated from growing databases of structural RNAs. Good results have been reported for discriminative statistical methods using complex nearest-neighbor models, including CONTRAfold, Simfold, and ContextFold. Little work has been reported on generative probabilistic models (stochastic context-free grammars [SCFGs]) of comparable complexity, although probabilistic models are generally easier to train and to use. To explore a range of probabilistic models of increasing complexity, and to directly compare probabilistic, thermodynamic, and discriminative approaches, we created TORNADO, a computational tool that can parse a wide spectrum of RNA grammar architectures (including the standard nearest-neighbor model and more) using a generalized super-grammar that can be parameterized with probabilities, energies, or arbitrary scores. By using TORNADO, we find that probabilistic nearest-neighbor models perform comparably to (but not significantly better than) discriminative methods. We find that complex statistical models are prone to overfitting RNA structure and that evaluations should use structurally nonhomologous training and test data sets. Overfitting has affected at least one published method (ContextFold). The most important barrier to improving statistical approaches for RNA secondary structure prediction is the lack of diversity of well-curated single-sequence RNA secondary structures in current RNA databases.

Thermodynamically stable RNA three-way junction for constructing multifunctional nanoparticles for delivery of therapeutics

RNA nanoparticles have applications in the treatment of cancers and viral infection; however, the instability of RNA nanoparticles has hindered their development for therapeutic applications. The lack of covalent linkage or crosslinking in nanoparticles causes dissociation in vivo. Here we show that the packaging RNA of bacteriophage phi29 DNA packaging motor can be assembled from 3-6 pieces of RNA oligomers without the use of metal salts. Each RNA oligomer contains a functional module that can be a receptor-binding ligand, aptamer, short interfering RNA or ribozyme. When mixed together, they self-assemble into thermodynamically stable tri-star nanoparticles with a three-way junction core. These nanoparticles are resistant to 8 M urea denaturation, are stable in serum and remain intact at extremely low concentrations. The modules remain functional in vitro and in vivo, suggesting that the three-way junction core can be used as a platform for building a variety of multifunctional nanoparticles. We studied 25 different three-way junction motifs in biological RNA and found only one other motif that shares characteristics similar to the three-way junction of phi29 pRNA.

Understanding the transcriptome through RNA structure

RNA structure is crucial for gene regulation and function. In the past, transcriptomes have largely been parsed by primary sequences and expression levels, but it is now becoming feasible to annotate and compare transcriptomes based on RNA structure. In addition to computational prediction methods, the recent advent of experimental techniques to probe RNA structure by high-throughput sequencing has enabled genome-wide measurements of RNA structure and has provided the first picture of the structural organization of a eukaryotic transcriptome - the 'RNA structurome'. With additional advances in method refinement and interpretation, structural views of the transcriptome should help to identify and validate regulatory RNA motifs that are involved in diverse cellular processes and thereby increase understanding of RNA function.